Analysis of Electromagnetic Force and Torque in High-Tc Superconducting Levitation Based on the Advanced Mirror Image Method

This research deals with theoretical evaluation of electromagnetic force and torque acting on a permanent magnet (PM) above a high-T_c superconductor (HTSC). While, as one potential application of HTSC magnetic levitation, HTSC bearings for energy storage flywheels are expected, it has not yet been theoretically clear whether HTSC levitation can work as an efficient bearing. In this research, force and torque acting on a PM above a HTSC were evaluated by the advanced mirror image method, which is based on the fact that magnetic flux at the field-cooling is trapped in type-II superconductors. Numerical results based on the above method showed good agreements with experimental ones. For a magnetic dipole over a flat ideal HTSC, the exact analytical solution of the force and torque was obtained as functions of the displacement and the Euler angle. This solution shows that the force and torque acting on the PM are theoretically equivalent to ones acting on a rigid body supported by an overhung elastic shaft, and gives the magnetic flexural rigidity of the HTSC levitation.